Speaking to CBS Evening News anchor Scott Pelley, Dolan said he was not certain what the next step would be once Pope Benedict XVI resigns.

“This hasn’t happened in six centuries,” Dolan said. “Now, we know what happens when the pope dies. Whether the same protocol will kick in, I don’t know. We’re waiting to see.”

Dolan told Pelley he expects the College of Cardinals to convene on March 1 since, with no pope in office, the College of Cardinals would be in charge of the day-to-day leadership functions of the Church.

Dolan said he will travel to Rome to vote in the conclave, a secret meeting held in the Sistine Chapel where cardinals cast ballots to elect a new pope.

“It’s awesome,” Dolan said. “I’ve known since becoming cardinal the awesome responsibility of helping choose a new pope.”

“There’s a bit of sadness. It’s like watching your own dad get old and admit that he’s not up to all the duties that being the head of the family involves and there’s a somberness there,” he said. “There’s a sadness there. But still there is an immense gratitude to God for the gift that he’s given us in Benedict XVI.”

He said his admiration for the Pope is now “even higher because of his humility.”

“I’ve just always admired him as a scholar, as a priest, as a holy man,” Dolan said. “I would presume that his esteem for the office as the successor of Saint Peter and the chief pastor of the Church Universal, that esteem is so high that in all humility he simply said he can’t do it anymore.”

Pope Benedict XVI has been known as a staunch conservative, at a time when many American Catholics have been looking for advancement on such issues as women in the priesthood. But Dolan told Pelley the pope must be conservative by nature.

“You have to realize, Scott, that the job description of the pope is to conserve, you know, to conserve the patrimony of the faith,” he said. “So it shouldn’t surprise anybody that the pope would be conservative, in the best sense of the word.”

When Pelley asked Dolan if the College of Cardinals would choose another conservative pope, Dolan said the college would likely just choose the best person for the job.

“I think Catholics in general, and certainly the College of Cardinals, would look for a man who is able to articulate the truths of the faith in a compelling and credible way; a man of deep piety who knows the Church Universal, and the needs of the people throughout the world,” Dolan said.

There are several papal contenders, but no obvious front-runners. When asked if he would be considered for the papacy, Dolan said it was “highly improbable.”